No, that's a very poor definition. That more closely describes vigilance.

A fear of things that are highly unlikely to happen is very often how we keep KEEP those things unlikely, as long as that fear isn't debilitating. It's why we have fire extinguishers, and why we don't have more incidents like the Challenger disaster.

I prefer this dictionary definition of paranoia:
"suspicion and mistrust of people or their actions without evidence or justification."